Smelly parallel MCMC chains

Monte Carlo (MC) methods are useful tools for Bayesian inference and stochastic optimization that have been widely applied in signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information, thus yielding a faster exploration of the state space. The interaction is carried out generating a dynamic repulsion among the “smelly” parallel chains that takes into account the entire population of current states. The ergodicity of the scheme and its relationship with other sampling methods are discussed. Numerical results show the advantages of the proposed approach in terms of mean square error, robustness w.r.t. to initial values and parameter choice.